# Asymmetric Return and Volatility Transmission in Conventional and Islamic Equities

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Bivariate VAR-EGARCH Model

#### 2.2. Multivariate VAR-EGARCH Model

_{i,t}is the standard innovation (i.e., ${z}_{i,t}=\text{}{\mathsf{\epsilon}}_{i,t}/{\mathsf{\sigma}}_{i,t}$). Equation (10) describes the return in each market as the function of its own previous returns and also of cross-market returns. If ${\mathsf{\beta}}_{i,j}$ is significant then market i leads market j. Equation (11) is conditional variance, which is a function of conditional variance at previous lags and is used to accommodate the asymmetric relation between stock returns and volatility changes. The function ${f}_{j}\left({z}_{j,\text{}t-1}\right)$ is made to account for both the magnitude and sign of ${z}_{j}$. The component of ${f}_{j}\left({z}_{j,t-1}\right)$, i.e., $\left(\left|{Z}_{j,t-1}\right|-E\left|{Z}_{j,t-1}\right|\right)$ represents magnitude effect and ${Z}_{j,t-1}$ sign effect, so that if ${Z}_{j,t-1}<0$ the slope of the function will be equal to $-1\text{}+\text{}{\mathsf{\tau}}_{j}$ whereas for ${Z}_{j,t-1}>0$ the slope becomes $1\text{}+\text{}{\mathsf{\tau}}_{j}$; for a shock to be positive, the value of ${Z}_{j,t-1}$ must be greater than its own expectation and vice versa. The coefficient of ${f}_{j}\left({z}_{j,\text{}t-1}\right)$, that is, ${\mathsf{\alpha}}_{i,j}$, measures cross-market spillover, which may be either symmetric or asymmetric depending upon ${\mathsf{\tau}}_{j}$, which is the coefficient of ${Z}_{j,t-1}$. The persistence of the conditional variance is measured by ${\mathsf{\gamma}}_{i}$ and for unconditional variance to be finite $\mathsf{\gamma}<1$ must hold. Equation (12) hence allows for standardized own and cross-market innovation to influence the conditional variance in each market asymmetrically. To, estimate these parameters we assume that they are normally distributed, taking the log of the probability density function of the parameters of system the likelihood for multivariate VAR-EGARCH model can be written as

_{t}is the 3 × 3 time varying conditional variance-covariance matrix with diagonal elements given by Equation (2) for i = 1, 2, 3; and cross-diagonal elements are given by Equation (4) for i, j = 1, 2, 3 and i ≠ j.

## 3. Data

- The total debt divided by trailing 24-month average market capitalization,
- The sum of a company’s cash and interest-bearing securities divided by trailing 24-month average market capitalization,
- The accounts receivables divided by trailing 24-month average market capitalization.

## 4. Results and Discussion

#### 4.1. Intra-Market Spillover among Islamic and Conventional Equities

#### 4.2. Inter-Market Spillover Effects

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## Appendix A

Japan | United States | United Kingdom | |||||||||||||

${\mathsf{\beta}}_{1,\mathrm{o}}$ | −0.0217 ** | ${\beta}_{1,o}$ | −0.0162 * | ${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0042 | ${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0004 | ${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0227 ** | ${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0231 ** | ||||

${\mathsf{\beta}}_{1,1}$ | −0.2734 *** | ${\beta}_{2,1}$ | −0.4768 *** | ${\mathsf{\beta}}_{1,1}$ | 0.0255 | ${\mathsf{\beta}}_{2,1}$ | 0.0368 | ${\mathsf{\beta}}_{1,1}$ | −0.1405 ** | ${\mathsf{\beta}}_{2,1}$ | −0.2576 *** | ||||

${\mathsf{\beta}}_{1,2}$ | 0.2695 *** | ${\beta}_{2,2}$ | 0.4580 *** | ${\mathsf{\beta}}_{1,2}$ | 0.1454 *** | ${\mathsf{\beta}}_{2,2}$ | −0.0371 | ${\mathsf{\beta}}_{1,2}$ | 0.1097 ** | ${\mathsf{\beta}}_{2,2}$ | 0.1930 *** | ||||

${\mathsf{\gamma}}_{10}$ | −0.0209 *** | ${\gamma}_{20}$ | −0.0173 *** | ${\mathsf{\gamma}}_{10}$ | −0.0672 | ${\mathsf{\gamma}}_{20}$ | −0.0409 | ${\mathsf{\gamma}}_{10}$ | −0.0305 *** | ${\mathsf{\gamma}}_{20}$ | −0.0220 *** | ||||

${\mathsf{\gamma}}_{11}$ | 0.9759 *** | ${\gamma}_{21}$ | −0.0773 *** | ${\mathsf{\gamma}}_{11}$ | 0.9690 *** | ${\mathsf{\gamma}}_{21}$ | 0.0487 *** | ${\mathsf{\gamma}}_{11}$ | 0.9818 *** | ${\mathsf{\gamma}}_{21}$ | 0.0097 | ||||

${\mathsf{\gamma}}_{12}$ | 0.1321 *** | ${\gamma}_{22}$ | 0.9776 *** | ${\mathsf{\gamma}}_{12}$ | −0.0124 | ${\mathsf{\gamma}}_{22}$ | 0.9693 *** | ${\mathsf{\gamma}}_{12}$ | 0.0474 ** | ${\mathsf{\gamma}}_{22}$ | 0.9847 *** | ||||

${\mathsf{\tau}}_{C}$ | −0.0846 *** | ${\tau}_{I}$ | −0.0217 * | ${\mathsf{\tau}}_{C}$ | −0.6667 *** | ${\mathsf{\tau}}_{I}$ | −0.5451 *** | ${\mathsf{\tau}}_{C}$ | −0.4798 *** | ${\mathsf{\tau}}_{I}$ | −0.3222 *** | ||||

Correlation Coefficients | |||||||||||||||

${\rho}_{1,2}$ | 0.9458 *** | ${\mathsf{\rho}}_{2,1}$ | 0.9458 *** | ${\mathsf{\rho}}_{1,2}$ | 0.8487 *** | ${\mathsf{\rho}}_{2,1}$ | 0.8487 *** | ${\mathsf{\rho}}_{1,2}$ | 0.9492 *** | ${\mathsf{\rho}}_{2,1}$ | 0.9492 *** | ||||

Residual Diagnostics | |||||||||||||||

AC(10) Residual | 0.01854 | 0.02119 | AC(12) Residual | 0.01971 | 0.01099 | AC(10) Residual | 0.01128 | 0.01450 | |||||||

AC(10) Squared Residual | 0.00570 | 0.00722 | AC(12) Squared Residual | 0.00130 | 0.00358 | AC(10) Squared Residual | 0.00803 | 0.00464 |

Japan | United States | United Kingdom | ||||||||||||||

${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0003 | ${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0007 | ${\beta}_{1,o}$ | −0.0056 | ${\mathsf{\beta}}_{1,\mathrm{o}}$ | −0.0006 | ${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0027 | ${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0091 | |||||

${\mathsf{\beta}}_{1,1}$ | −0.1681 * | ${\mathsf{\beta}}_{2,1}$ | 0.1897 ** | ${\beta}_{1,1}$ | 0.0883 | ${\mathsf{\beta}}_{2,1}$ | 0.2021 ** | ${\mathsf{\beta}}_{1,1}$ | 0.2360 * | ${\mathsf{\beta}}_{2,1}$ | 0.1553 | |||||

${\mathsf{\beta}}_{1,2}$ | 0.0481 | ${\mathsf{\beta}}_{2,2}$ | 0.0520 | ${\beta}_{1,2}$ | 0.1318 ** | ${\mathsf{\beta}}_{2,2}$ | −0.0973 | ${\mathsf{\beta}}_{1,2}$ | −0.2532 ** | ${\mathsf{\beta}}_{2,2}$ | −0.1886 | |||||

${\mathsf{\gamma}}_{10}$ | −0.0562 *** | ${\mathsf{\gamma}}_{20}$ | −0.0529 *** | ${\gamma}_{10}$ | −0.1403 *** | ${\mathsf{\gamma}}_{20}$ | −0.1542 *** | ${\mathsf{\gamma}}_{10}$ | −0.0133 *** | ${\mathsf{\gamma}}_{20}$ | −0.0136 *** | |||||

${\mathsf{\gamma}}_{11}$ | 0.9473 *** | ${\mathsf{\gamma}}_{21}$ | 0.1025 ** | ${\gamma}_{11}$ | 0.9479 *** | ${\mathsf{\gamma}}_{21}$ | 0.0873 ** | ${\mathsf{\gamma}}_{11}$ | 0.9874 *** | ${\mathsf{\gamma}}_{21}$ | 0.0048 | |||||

${\mathsf{\gamma}}_{12}$ | 0.0176 | ${\mathsf{\gamma}}_{22}$ | 0.9536 *** | ${\gamma}_{12}$ | 0.0119 | ${\mathsf{\gamma}}_{22}$ | 0.9295 *** | ${\mathsf{\gamma}}_{12}$ | 0.0867 ** | ${\mathsf{\gamma}}_{22}$ | 0.9878 *** | |||||

${\mathsf{\tau}}_{C}$ | −0.2857 *** | ${\mathsf{\tau}}_{I}$ | −0.2746 ** | ${\mathsf{\tau}}_{C}$ | −0.3791 *** | ${\mathsf{\tau}}_{I}$ | −0.0340 *** | ${\mathsf{\tau}}_{C}$ | −0.0529 *** | ${\mathsf{\tau}}_{I}$ | 0.9673 *** | |||||

Correlation Coefficients | ||||||||||||||||

${\mathsf{\rho}}_{1,2}$ | 0.6719 *** | ${\mathsf{\rho}}_{2,1}$ | 0.6719 *** | ${\mathsf{\rho}}_{1,2}$ | 0.8940 *** | ${\mathsf{\rho}}_{2,1}$ | 0.8940 *** | ${\mathsf{\rho}}_{1,2}$ | 0.9673 *** | ${\mathsf{\rho}}_{2,1}$ | 0.8695 *** | |||||

Residual Diagnostics | ||||||||||||||||

AC(10) Residual | 0.00477 | 0.01771 | AC(12) Residual | 0.04776 | 0.00726 | AC(10) Residual | 0.01732 | 0.05216 | ||||||||

AC(10) Squared Residual | 0.03718 | 0.03288 | AC(12) Squared Residual | 0.00251 | 0.00221 | AC(10) Squared Residual | 0.00250 | 0.00950 |

Japan | United States | United Kingdom | |||||||||||||||

${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0002 | ${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0007 | ${\beta}_{1,o}$ | −0.0292 | ${\mathsf{\beta}}_{1,\mathrm{o}}$ | −0.0260 | ${\mathsf{\beta}}_{1,\mathrm{o}}$ | −0.0182 | ${\beta}_{1,o}$ | −0.0183 | ||||||

${\mathsf{\beta}}_{1,1}$ | −0.1681 * | ${\mathsf{\beta}}_{2,1}$ | 0.1897 ** | ${\beta}_{1,1}$ | −0.0629 | ${\mathsf{\beta}}_{2,1}$ | −0.0213 | ${\mathsf{\beta}}_{1,1}$ | −0.1608 | ${\beta}_{2,1}$ | −0.1267 | ||||||

${\mathsf{\beta}}_{1,2}$ | 0.0481 | ${\mathsf{\beta}}_{2,2}$ | 0.0521 | ${\beta}_{1,2}$ | 0.1926 ** | ${\mathsf{\beta}}_{2,2}$ | −0.1586 ** | ${\mathsf{\beta}}_{1,2}$ | 0.2522 | ${\beta}_{2,2}$ | 0.2161 | ||||||

${\mathsf{\gamma}}_{10}$ | −0.0562 *** | ${\mathsf{\gamma}}_{20}$ | −0.0529 *** | ${\gamma}_{10}$ | −0.0273 *** | ${\mathsf{\gamma}}_{20}$ | −0.0226 ** | ${\mathsf{\gamma}}_{10}$ | −0.0474 ** | ${\gamma}_{20}$ | −0.0345 ** | ||||||

${\mathsf{\gamma}}_{11}$ | 0.9473 *** | ${\mathsf{\gamma}}_{21}$ | 0.1025 ** | ${\gamma}_{11}$ | 0.9749 *** | ${\mathsf{\gamma}}_{21}$ | 0.1241 ** | ${\mathsf{\gamma}}_{11}$ | 0.9744 *** | ${\gamma}_{21}$ | 0.0117 | ||||||

${\mathsf{\gamma}}_{12}$ | 0.01769 | ${\mathsf{\gamma}}_{22}$ | 0.9536 *** | ${\gamma}_{12}$ | 0.1461 ** | ${\mathsf{\gamma}}_{22}$ | 0.9740 *** | ${\mathsf{\gamma}}_{12}$ | 0.0005 ** | ${\gamma}_{22}$ | 0.9805 *** | ||||||

${\mathsf{\tau}}_{C}$ | −0.2857 *** | ${\mathsf{\tau}}_{I}$ | −0.2746 ** | ${\mathsf{\tau}}_{C}$ | −0.7042 *** | ${\mathsf{\tau}}_{I}$ | −0.6611 ** | ${\mathsf{\tau}}_{C}$ | −0.7101 | ${\tau}_{I}$ | −0.9452 | ||||||

Correlation Coefficients | |||||||||||||||||

${\mathsf{\rho}}_{1,2}$ | 0.7709 *** | ${\mathsf{\rho}}_{2,1}$ | 0.7709 *** | ${\mathsf{\rho}}_{1,2}$ | 0.8980 *** | ${\mathsf{\rho}}_{2,1}$ | 0.8980 *** | ${\mathsf{\rho}}_{1,2}$ | 0.8744 *** | ${\rho}_{2,1}$ | 0.8744 *** | ||||||

Residual Diagnostics | |||||||||||||||||

AC(10) Residual | 0.00477 | 0.01771 | AC(12) Residual | 0.00406 | 0.00173 | AC(10) Residual | 0.08458 | 0.09864 | |||||||||

AC(10) Squared Residual | 0.00079 | 0.00097 | AC(12) Squared Residual | 0.00840 | 0.00399 | AC(10) Squared Residual | 0.00783 | 0.00254 |

United States | United Kingdom | Japan | ||||||

${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0103 | ${\mathsf{\beta}}_{2,\mathrm{o}}$ | 0.0153 ** | ${\mathsf{\beta}}_{3,\mathrm{o}}$ | −0.0039 | |||

${\mathsf{\beta}}_{1,1}$ | −0.0077 | ${\mathsf{\beta}}_{2,1}$ | 0.3144 *** | ${\mathsf{\beta}}_{3,1}$ | 0.3951 *** | |||

${\mathsf{\beta}}_{1,2}$ | 0.0232 | ${\mathsf{\beta}}_{2,2}$ | −0.1020 ** | ${\mathsf{\beta}}_{3,2}$ | 0.1284 *** | |||

${\mathsf{\beta}}_{1,3}$ | −0.0129 | ${\mathsf{\beta}}_{2,3}$ | −0.0353 ** | ${\mathsf{\beta}}_{3,3}$ | −0.0188 | |||

${\mathsf{\alpha}}_{10}$ | −0.0280 *** | ${\mathsf{\alpha}}_{20}$ | −0.0277 *** | ${\mathsf{\alpha}}_{30}$ | −0.0238 *** | |||

${\mathsf{\alpha}}_{11}$ | 0.0812 *** | ${\mathsf{\alpha}}_{21}$ | 0.0315 *** | ${\mathsf{\alpha}}_{31}$ | 0.0278 ** | |||

${\mathsf{\alpha}}_{12}$ | 0.0631 *** | ${\mathsf{\alpha}}_{22}$ | 0.0934 *** | ${\mathsf{\alpha}}_{32}$ | 0.0615 *** | |||

${\mathsf{\alpha}}_{13}$ | 0.0443 ** | ${\mathsf{\alpha}}_{23}$ | 0.0155 | ${\mathsf{\alpha}}_{33}$ | 0.1469 *** | |||

${\mathsf{\tau}}_{1}$ | −0.0340 *** | ${\mathsf{\tau}}_{2}$ | −0.3050 ** | ${\mathsf{\tau}}_{3}$ | −0.1127 * | |||

${\mathsf{\gamma}}_{1}$ | 0.9788 *** | ${\mathsf{\gamma}}_{2}$ | 0.9817 *** | ${\mathsf{\gamma}}_{3}$ | 0.9764 *** | |||

Correlation Coefficients | ||||||||

${\mathsf{\rho}}_{1,2}$ | 0.0683 *** | ${\mathsf{\rho}}_{2,3}$ | 0.1567 *** | ${\mathsf{\rho}}_{1,3}$ | 0.3352 *** | |||

Residual Diagnostics | ||||||||

AC(10) Residual | 0.01663 | AC(10) Residual | 0.01055 | AC(10) Residual | 0.01739 | |||

AC(10) Squared Residual | 0.00790 | AC(10) Squared Residual | 0.00353 | AC(10) Squared Residual | 0.00378 |

United States | United Kingdom | Japan | ||||||

${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0101 * | ${\mathsf{\beta}}_{2,\mathrm{o}}$ | 0.0141 * | ${\mathsf{\beta}}_{3,\mathrm{o}}$ | −0.0098 | |||

${\mathsf{\beta}}_{1,1}$ | 0.3394 *** | ${\mathsf{\beta}}_{2,1}$ | 0.5718 *** | ${\mathsf{\beta}}_{3,1}$ | 0.6517 *** | |||

${\mathsf{\beta}}_{1,2}$ | −0.0832 *** | ${\mathsf{\beta}}_{2,2}$ | −0.2604 *** | ${\mathsf{\beta}}_{3,2}$ | −0.0402 | |||

${\mathsf{\beta}}_{1,3}$ | −0.0762 *** | ${\mathsf{\beta}}_{2,3}$ | −0.1167 *** | ${\mathsf{\beta}}_{3,3}$ | −0.1128 *** | |||

${\mathsf{\alpha}}_{10}$ | −0.0512 *** | ${\mathsf{\alpha}}_{20}$ | −0.0553 *** | ${\mathsf{\alpha}}_{30}$ | −0.0240 *** | |||

${\mathsf{\alpha}}_{11}$ | 0.0636 *** | ${\mathsf{\alpha}}_{21}$ | 0.0464 *** | ${\mathsf{\alpha}}_{31}$ | 0.0357 *** | |||

${\mathsf{\alpha}}_{12}$ | 0.0790 *** | ${\mathsf{\alpha}}_{22}$ | 0.1105 *** | ${\mathsf{\alpha}}_{32}$ | 0.0524 *** | |||

${\mathsf{\alpha}}_{13}$ | 0.0121 | ${\mathsf{\alpha}}_{23}$ | −0.0056 | ${\mathsf{\alpha}}_{33}$ | 0.1108 *** | |||

${\mathsf{\tau}}_{1}$ | −0.4675 *** | ${\mathsf{\tau}}_{2}$ | −0.1168 | ${\mathsf{\tau}}_{3}$ | −0.1832 ** | |||

${\mathsf{\gamma}}_{1}$ | 0.9768 *** | ${\mathsf{\gamma}}_{2}$ | 0.9697 *** | ${\mathsf{\gamma}}_{3}$ | 0.9779 *** | |||

Correlation Coefficients | ||||||||

${\mathsf{\rho}}_{1,2}$ | 0.6284 ** | ${\mathsf{\rho}}_{2,3}$ | 0.3870 *** | ${\mathsf{\rho}}_{1,3}$ | 0.1874 *** | |||

Residual Diagnostics | ||||||||

AC(10) Residual | 0.01087 | AC(10) Residual | 0.02988 | AC(10) Residual | 0.02535 | |||

AC(10) Squared Residual | 0.00696 | AC(10) Squared Residual | 0.00885 | AC(10) Squared Residual | 0.00421 |

United States | United Kingdom | Japan | ||||||

${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0134 | ${\mathsf{\beta}}_{2,\mathrm{o}}$ | −0.0044 | ${\mathsf{\beta}}_{3,\mathrm{o}}$ | −0.0103 | |||

${\mathsf{\beta}}_{1,1}$ | −0.0606 * | ${\mathsf{\beta}}_{2,1}$ | 0.5033 *** | ${\mathsf{\beta}}_{3,1}$ | 0.4296 *** | |||

${\mathsf{\beta}}_{1,2}$ | 0.0091 | ${\mathsf{\beta}}_{2,2}$ | −0.2592 | ${\mathsf{\beta}}_{3,2}$ | 0.1248 *** | |||

${\mathsf{\beta}}_{1,3}$ | 0.0082 | ${\mathsf{\beta}}_{2,3}$ | 0.0535 ** | ${\mathsf{\beta}}_{3,3}$ | −0.1781 *** | |||

${\mathsf{\alpha}}_{10}$ | −0.0288 *** | ${\mathsf{\alpha}}_{20}$ | −0.0153 *** | ${\mathsf{\alpha}}_{30}$ | −0.0629 *** | |||

${\mathsf{\alpha}}_{11}$ | 0.0581 ** | ${\mathsf{\alpha}}_{21}$ | 0.0290 ** | ${\mathsf{\alpha}}_{31}$ | 0.0260 ** | |||

${\mathsf{\alpha}}_{12}$ | 0.0407 ** | ${\mathsf{\alpha}}_{22}$ | 0.0740 *** | ${\mathsf{\alpha}}_{32}$ | 0.0206 | |||

${\mathsf{\alpha}}_{13}$ | 0.0296 ** | ${\mathsf{\alpha}}_{23}$ | 0.0254 * | ${\mathsf{\alpha}}_{33}$ | 0.1786 *** | |||

${\mathsf{\tau}}_{1}$ | −0.2173 *** | ${\mathsf{\tau}}_{2}$ | −0.4677 *** | ${\mathsf{\tau}}_{3}$ | −0.4659 *** | |||

${\mathsf{\gamma}}_{1}$ | 0.9799 *** | ${\mathsf{\gamma}}_{2}$ | 0.9831 *** | ${\mathsf{\gamma}}_{3}$ | 0.9542 *** | |||

Correlation Coefficients | ||||||||

${\mathsf{\rho}}_{1,2}$ | 0.0494 ** | ${\mathsf{\rho}}_{2,3}$ | 0.1199 *** | ${\mathsf{\rho}}_{1,3}$ | 0.6357 *** | |||

Residual Diagnostics | ||||||||

AC(10) Residual | 0.01948 | AC(10) Residual | 0.02327 | AC(10) Residual | 0.01360 | |||

AC(10) Squared Residual | 0.00698 | AC(10) Squared Residual | 0.00593 | AC(10) Squared Residual | 0.00898 |

United States | United Kingdom | Japan | ||||||

${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0059 | ${\mathsf{\beta}}_{2,\mathrm{o}}$ | −0.0004 | ${\mathsf{\beta}}_{3,\mathrm{o}}$ | −0.0112 | |||

${\mathsf{\beta}}_{1,1}$ | 0.3678 *** | ${\mathsf{\beta}}_{2,1}$ | 0.8221 *** | ${\mathsf{\beta}}_{3,1}$ | 0.6923 *** | |||

${\mathsf{\beta}}_{1,2}$ | −0.1676 *** | ${\mathsf{\beta}}_{2,2}$ | −0.5247 *** | ${\mathsf{\beta}}_{3,2}$ | −0.0398 | |||

${\mathsf{\beta}}_{1,3}$ | −0.0558 *** | ${\mathsf{\beta}}_{2,3}$ | −0.0682 ** | ${\mathsf{\beta}}_{3,3}$ | −0.2819 *** | |||

${\mathsf{\alpha}}_{10}$ | −0.0224 *** | ${\mathsf{\alpha}}_{20}$ | −0.0120 *** | ${\mathsf{\alpha}}_{30}$ | −0.0860 *** | |||

${\mathsf{\alpha}}_{11}$ | 0.0852 *** | ${\mathsf{\alpha}}_{21}$ | 0.0580 *** | ${\mathsf{\alpha}}_{31}$ | 0.0471 ** | |||

${\mathsf{\alpha}}_{12}$ | 0.0051 | ${\mathsf{\alpha}}_{22}$ | 0.0244 *** | ${\mathsf{\alpha}}_{32}$ | 0.0007 | |||

${\mathsf{\alpha}}_{13}$ | 0.0138 | ${\mathsf{\alpha}}_{23}$ | 0.0166 | ${\mathsf{\alpha}}_{33}$ | 0.1969 *** | |||

${\mathsf{\tau}}_{1}$ | −0.1841 *** | ${\mathsf{\tau}}_{2}$ | −0.2023 ** | ${\mathsf{\tau}}_{3}$ | −0.4570 *** | |||

${\mathsf{\gamma}}_{1}$ | 0.9857 *** | ${\mathsf{\gamma}}_{2}$ | 0.9875 *** | ${\mathsf{\gamma}}_{3}$ | 0.9352 *** | |||

Correlation Coefficients | ||||||||

${\mathsf{\rho}}_{1,2}$ | 0.8588 *** | ${\mathsf{\rho}}_{2,3}$ | 0.2504 *** | ${\mathsf{\rho}}_{1,3}$ | 0.1331 *** | |||

Residual Diagnostics | ||||||||

AC(10) Residual | 0.01305 | AC(10) Residual | 0.01883 | AC(10) Residual | 0.01063 | |||

AC(10) Squared Residual | 0.00590 | AC(10) Squared Residual | 0.00850 | AC(10) Squared Residual | 0.00407 |

United States | United Kingdom | Japan | ||||||

${\mathsf{\beta}}_{1,\mathrm{o}}$ | −0.0110 | ${\mathsf{\beta}}_{2,\mathrm{o}}$ | −0.0307 ** | ${\mathsf{\beta}}_{3,\mathrm{o}}$ | 0.0242 | |||

${\mathsf{\beta}}_{1,1}$ | −0.0239 | ${\mathsf{\beta}}_{2,1}$ | 0.2790 *** | ${\mathsf{\beta}}_{3,1}$ | 0.3962 *** | |||

${\mathsf{\beta}}_{1,2}$ | 0.0943 * | ${\mathsf{\beta}}_{2,2}$ | 0.0325 | ${\mathsf{\beta}}_{3,2}$ | 0.1008 * | |||

${\mathsf{\beta}}_{1,3}$ | 0.0374 | ${\mathsf{\beta}}_{2,3}$ | 0.0092 | ${\mathsf{\beta}}_{3,3}$ | −0.2105 ** | |||

${\mathsf{\alpha}}_{10}$ | −0.1844 | ${\mathsf{\alpha}}_{20}$ | −0.1529 | ${\mathsf{\alpha}}_{30}$ | −0.0538 * | |||

${\mathsf{\alpha}}_{11}$ | 0.0082 | ${\mathsf{\alpha}}_{21}$ | 0.0039 | ${\mathsf{\alpha}}_{31}$ | 0.0024 | |||

${\mathsf{\alpha}}_{12}$ | 0.0121 | ${\mathsf{\alpha}}_{22}$ | 0.0215 | ${\mathsf{\alpha}}_{32}$ | 0.0080 | |||

${\mathsf{\alpha}}_{13}$ | 0.1671 ** | ${\mathsf{\alpha}}_{23}$ | 0.0659 | ${\mathsf{\alpha}}_{33}$ | 0.0801 ** | |||

${\mathsf{\tau}}_{1}$ | −0.2581 | ${\mathsf{\tau}}_{2}$ | −0.4031 | ${\mathsf{\tau}}_{3}$ | −0.2497 | |||

${\mathsf{\gamma}}_{1}$ | 0.9121 *** | ${\mathsf{\gamma}}_{2}$ | 0.9182 *** | ${\mathsf{\gamma}}_{3}$ | 0.9673 *** | |||

Correlation Coefficients | ||||||||

${\mathsf{\rho}}_{1,2}$ | −0.0129 | ${\mathsf{\rho}}_{2,3}$ | 0.0907 * | ${\mathsf{\rho}}_{1,3}$ | 0.5256 *** | |||

Residual Diagnostics | ||||||||

AC(10) Residual | 0.03585 | AC(10) Residual | 0.03963 | AC(10) Residual | 0.02418 | |||

AC(10) Squared Residual | 0.00605 | AC(10) Squared Residual | 0.00042 | AC(10) Squared Residual | 0.00374 |

United States | United Kingdom | Japan | ||||||

${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0001 | ${\mathsf{\beta}}_{2,\mathrm{o}}$ | −0.0106 | ${\mathsf{\beta}}_{3,\mathrm{o}}$ | 0.0051 | |||

${\mathsf{\beta}}_{1,1}$ | 0.2802 *** | ${\mathsf{\beta}}_{2,1}$ | 0.6161 *** | ${\mathsf{\beta}}_{3,1}$ | 0.6846 *** | |||

${\mathsf{\beta}}_{1,2}$ | −0.0926 *** | ${\mathsf{\beta}}_{2,2}$ | −0.3553 *** | ${\mathsf{\beta}}_{3,2}$ | −0.0433 | |||

${\mathsf{\beta}}_{1,3}$ | −0.0303 *** | ${\mathsf{\beta}}_{2,3}$ | −0.0247 | ${\mathsf{\beta}}_{3,3}$ | −0.2857 *** | |||

${\mathsf{\alpha}}_{10}$ | −0.0712 *** | ${\mathsf{\alpha}}_{20}$ | −0.0520 | ${\mathsf{\alpha}}_{30}$ | −0.1316 ** | |||

${\mathsf{\alpha}}_{11}$ | 0.1030 *** | ${\mathsf{\alpha}}_{21}$ | 0.0748 *** | ${\mathsf{\alpha}}_{31}$ | 0.0605 *** | |||

${\mathsf{\alpha}}_{12}$ | −0.0141 | ${\mathsf{\alpha}}_{22}$ | 0.0094 | ${\mathsf{\alpha}}_{32}$ | −0.029 | |||

${\mathsf{\alpha}}_{13}$ | −0.0048 | ${\mathsf{\alpha}}_{23}$ | −0.0163 | ${\mathsf{\alpha}}_{33}$ | 0.1538 *** | |||

${\mathsf{\tau}}_{1}$ | −0.7891 *** | ${\mathsf{\tau}}_{2}$ | −0.3245 * | ${\mathsf{\tau}}_{3}$ | −0.4148 ** | |||

${\mathsf{\gamma}}_{1}$ | 0.9676 *** | ${\mathsf{\gamma}}_{2}$ | 0.9679 *** | ${\mathsf{\gamma}}_{3}$ | 0.9236 *** | |||

Correlation Coefficients | ||||||||

${\mathsf{\rho}}_{1,2}$ | 0.8404 *** | ${\mathsf{\rho}}_{2,3}$ | 0.1763 *** | ${\mathsf{\rho}}_{1,3}$ | 0.2879 *** | |||

Residual Diagnostics | ||||||||

AC(10) Residual | 0.01134 | AC(10) Residual | 0.03414 | AC(10) Residual | 0.01297 | |||

AC(10) Squared Residual | 0.00926 | AC(10) Squared Residual | 0.03226 | AC(10) Squared Residual | 0.00569 |

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Statistics | Islamic | Conventional | ||||
---|---|---|---|---|---|---|

Japan | USA | UK | Japan | USA | UK | |

Mean | 0.007 | 0.014 | 0.010 | 0.002 | 0.010 | 0.010 |

Median | 0.006 | 0.016 | 0.022 | 0.004 | 0.032 | 0.017 |

Std. Dev. | 0.620 | 0.543 | 0.562 | 0.608 | 0.424 | 0.592 |

Skewness | −0.053 | −0.133 | −0.158 | −0.017 | −0.402 | −0.102 |

Kurtosis | 6.703 | 9.642 | 11.510 | 7.244 | 10.246 | 9.518 |

Jarque-Bera | 2982 *** | 9606 *** | 15768 *** | 3916 *** | 11554 *** | 9245 *** |

AC(10) Residual | 0.0100 | 0.0240 | 0.0170 | 0.0100 | 0.0170 | 0.0250 |

AC(10) Squared Residual | 0.1180 | 0.1830 | 0.2020 | 0.1580 | 0.1430 | 0.1910 |

Arch | 0.1701 *** | 0.2131 *** | 0.1902 *** | 0.1635 *** | 0.2210 *** | 0.1931 *** |

Size bias | −0.0031 | −0.0933 * | −0.1202 * | −0.0125 | −0.0342 | −0.0981 * |

Negative sign bias | −0.3527 *** | −0.7095 *** | −0.6834 *** | −0.3736 *** | −0.5264 *** | −0.7262 *** |

Positive sign bias | 0.2875 *** | 0.1603 *** | 0.2543 *** | 0.2835 *** | 0.2382 *** | 0.2897 *** |

Japan | United States | United Kingdom | |||||||||

${\mathsf{\beta}}_{1,0}$ | −0.0125 ** | ${\mathsf{\beta}}_{1,0}$ | −0.0077 | ${\mathsf{\beta}}_{1,0}$ | 0.0045 | ${\mathsf{\beta}}_{1,0}$ | 0.0061 | ${\mathsf{\beta}}_{1,0}$ | 0.0109 * | ${\mathsf{\beta}}_{1,0}$ | 0.0101 |

${\mathsf{\beta}}_{1,1}$ | 0.3426 *** | ${\mathsf{\beta}}_{2,1}$ | −0.4983 *** | ${\mathsf{\beta}}_{1,1}$ | 0.0168 | ${\mathsf{\beta}}_{2,1}$ | 0.0519 ** | ${\mathsf{\beta}}_{1,1}$ | −0.0546 | ${\mathsf{\beta}}_{2,1}$ | 0.1367 *** |

${\mathsf{\beta}}_{1,2}$ | 0.2752 *** | ${\mathsf{\beta}}_{2,2}$ | 0.4157 *** | ${\mathsf{\beta}}_{1,2}$ | 0.1456 *** | ${\mathsf{\beta}}_{2,2}$ | −0.0808 ** | ${\mathsf{\beta}}_{1,2}$ | 0.0453 | ${\mathsf{\beta}}_{2,2}$ | 0.1075 ** |

${\mathsf{\gamma}}_{10}$ | −0.0213 *** | ${\mathsf{\gamma}}_{20}$ | −0.0187 *** | ${\mathsf{\gamma}}_{10}$ | −0.0401 *** | ${\mathsf{\gamma}}_{20}$ | −0.0317 *** | ${\mathsf{\gamma}}_{10}$ | −0.0234 *** | ${\mathsf{\gamma}}_{20}$ | −0.0196 *** |

${\mathsf{\gamma}}_{11}$ | 0.9768 *** | ${\mathsf{\gamma}}_{21}$ | −0.0469 *** | ${\mathsf{\gamma}}_{11}$ | 0.9791 *** | ${\mathsf{\gamma}}_{21}$ | 0.0182 ** | ${\mathsf{\gamma}}_{11}$ | 0.9829 *** | ${\mathsf{\gamma}}_{21}$ | 0.0051 * |

${\mathsf{\gamma}}_{12}$ | 0.1249 *** | ${\mathsf{\gamma}}_{22}$ | 0.9784 *** | ${\mathsf{\gamma}}_{12}$ | 0.0186 *** | ${\mathsf{\gamma}}_{22}$ | 0.9763 *** | ${\mathsf{\gamma}}_{12}$ | 0.0426 *** | ${\mathsf{\gamma}}_{22}$ | 0.9839 *** |

${\mathsf{\tau}}_{C}$ | −0.1305 *** | ${\mathsf{\tau}}_{I}$ | −0.1023 *** | ${\mathsf{\tau}}_{C}$ | −0.5661 *** | ${\mathsf{\tau}}_{I}$ | −0.6544 *** | ${\mathsf{\tau}}_{C}$ | −0.5986 *** | ${\mathsf{\tau}}_{I}$ | −0.4983 |

Correlation Coefficients | |||||||||||

${\mathsf{\rho}}_{1,2}$ | 0.6560 *** | ${\mathsf{\rho}}_{2,1}$ | 0.6560 *** | ${\mathsf{\rho}}_{1,2}$ | 0.8651 *** | ${\mathsf{\rho}}_{2,1}$ | 0.8651 *** | ${\mathsf{\rho}}_{1,2}$ | 0.8589 *** | ${\mathsf{\rho}}_{2,1}$ | 0.8589 *** |

Residual Diagnostics | |||||||||||

AC(10) Residual | 0.01628 | 0.02231 | AC(12) Residual | 0.00093 | 0.01600 | AC(10) Residual | −0.01268 | −0.01423 | |||

AC(10) Squared Residual | 0.00526 | 0.00174 | AC(12) Squared Residual | 0.03174 | 0.02518 | AC(10) Squared Residual | 0.01978 | 0.01112 |

United States | United Kingdom | Japan | ||||||

${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0089 | ${\mathsf{\beta}}_{2,\mathrm{o}}$ | 0.0054 | ${\mathsf{\beta}}_{3,\mathrm{o}}$ | −0.0018 | |||

${\mathsf{\beta}}_{1,1}$ | −0.0361 * | ${\mathsf{\beta}}_{2,1}$ | 0.3416 *** | ${\mathsf{\beta}}_{3,1}$ | 0.4092 *** | |||

${\mathsf{\beta}}_{1,2}$ | 0.0227 * | ${\mathsf{\beta}}_{2,2}$ | −0.1339 *** | ${\mathsf{\beta}}_{3,2}$ | 0.1307 *** | |||

${\mathsf{\beta}}_{1,3}$ | −0.0014 | ${\mathsf{\beta}}_{2,3}$ | −0.0091 | ${\mathsf{\beta}}_{3,3}$ | −0.0967 *** | |||

${\mathsf{\alpha}}_{10}$ | −0.0296 *** | ${\mathsf{\alpha}}_{20}$ | −0.0222 *** | ${\mathsf{\alpha}}_{30}$ | −0.0319 *** | |||

${\mathsf{\alpha}}_{11}$ | 0.0986 *** | ${\mathsf{\alpha}}_{21}$ | 0.0413 *** | ${\mathsf{\alpha}}_{31}$ | 0.0432 *** | |||

${\mathsf{\alpha}}_{12}$ | 0.0385 *** | ${\mathsf{\alpha}}_{22}$ | 0.0901 *** | ${\mathsf{\alpha}}_{32}$ | 0.0387 *** | |||

${\mathsf{\alpha}}_{13}$ | 0.0549 *** | ${\mathsf{\alpha}}_{23}$ | 0.0226 ** | ${\mathsf{\alpha}}_{33}$ | 0.1606 *** | |||

${\mathsf{\tau}}_{1}$ | −0.0482 *** | ${\mathsf{\tau}}_{2}$ | −0.4833 *** | ${\mathsf{\tau}}_{3}$ | −0.1802 *** | |||

${\mathsf{\gamma}}_{1}$ | 0.9776 *** | ${\mathsf{\gamma}}_{2}$ | 0.9821 *** | ${\mathsf{\gamma}}_{3}$ | 0.9716 *** | |||

Correlation Coefficients | ||||||||

${\mathsf{\rho}}_{1,2}$ | 0.0547 *** | ${\mathsf{\rho}}_{2,3}$ | 0.1318 *** | ${\mathsf{\rho}}_{1,3}$ | 0.4568 *** | |||

Residual Diagnostics | ||||||||

AC(10) Residual | 0.0166 | AC(10) Residual | 0.0154 | AC(10) Residual | 0.0125 | |||

AC(10) Squared Residual | 0.0043 | AC(10) Squared Residual | 0.0084 | AC(10) Squared Residual | 0.0093 |

United States | United Kingdom | Japan | ||||||

${\mathsf{\beta}}_{1,\mathrm{o}}$ | 0.0064 | ${\mathsf{\beta}}_{2,\mathrm{o}}$ | 0.0062 | ${\mathsf{\beta}}_{3,\mathrm{o}}$ | −0.0085 | |||

${\mathsf{\beta}}_{1,1}$ | 0.3144 *** | ${\mathsf{\beta}}_{2,1}$ | 0.5879 *** | ${\mathsf{\beta}}_{3,1}$ | 0.6815 *** | |||

${\mathsf{\beta}}_{1,2}$ | −0.0972 *** | ${\mathsf{\beta}}_{2,2}$ | −0.3106 *** | ${\mathsf{\beta}}_{3,2}$ | −0.0345 * | |||

${\mathsf{\beta}}_{1,3}$ | −0.0638 *** | ${\mathsf{\beta}}_{2,3}$ | −0.0907 *** | ${\mathsf{\beta}}_{3,3}$ | −0.1899 *** | |||

${\mathsf{\alpha}}_{10}$ | −0.0484 *** | ${\mathsf{\alpha}}_{20}$ | −0.0404 *** | ${\mathsf{\alpha}}_{30}$ | −0.0387 *** | |||

${\mathsf{\alpha}}_{11}$ | 0.0845 *** | ${\mathsf{\alpha}}_{21}$ | 0.0608 *** | ${\mathsf{\alpha}}_{31}$ | 0.0523 *** | |||

${\mathsf{\alpha}}_{12}$ | 0.0357 *** | ${\mathsf{\alpha}}_{22}$ | 0.0746 *** | ${\mathsf{\alpha}}_{32}$ | 0.0138 | |||

${\mathsf{\alpha}}_{13}$ | 0.0282 ** | ${\mathsf{\alpha}}_{23}$ | 0.0166 ** | ${\mathsf{\alpha}}_{33}$ | 0.1487 *** | |||

${\mathsf{\tau}}_{1}$ | −0.1429 *** | ${\mathsf{\tau}}_{2}$ | −0.4175 *** | ${\mathsf{\tau}}_{3}$ | −0.2374 *** | |||

${\mathsf{\gamma}}_{1}$ | 0.9756 *** | ${\mathsf{\gamma}}_{2}$ | 0.9728 *** | ${\mathsf{\gamma}}_{3}$ | 0.9675 *** | |||

Correlation Coefficients | ||||||||

${\mathsf{\rho}}_{1,2}$ | 0.7295 *** | ${\mathsf{\rho}}_{2,3}$ | 0.3199 *** | ${\mathsf{\rho}}_{1,3}$ | 0.1584 *** | |||

Residual Diagnostics | ||||||||

AC(10) Residual | 0.01552 | AC(10) Residual | 0.01046 | AC(10) Residual | 0.01775 | |||

AC(10) Squared Residual | 0.00926 | AC(10) Squared Residual | 0.00864 | AC(10) Squared Residual | 0.00173 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Umar, Z.; Suleman, T.
Asymmetric Return and Volatility Transmission in Conventional and Islamic Equities. *Risks* **2017**, *5*, 22.
https://doi.org/10.3390/risks5020022

**AMA Style**

Umar Z, Suleman T.
Asymmetric Return and Volatility Transmission in Conventional and Islamic Equities. *Risks*. 2017; 5(2):22.
https://doi.org/10.3390/risks5020022

**Chicago/Turabian Style**

Umar, Zaghum, and Tahir Suleman.
2017. "Asymmetric Return and Volatility Transmission in Conventional and Islamic Equities" *Risks* 5, no. 2: 22.
https://doi.org/10.3390/risks5020022